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Math Trailhead

Worksheet Exponent Rules

14.

(a) Simplify \(\displaystyle{\frac{n^{7}}{n^{15}}}\) and write your answer without using negative exponents.
(b) Simplify \(\displaystyle{\frac{n^{7}}{n^{-15}}}\) and write your answer without using negative exponents.
(c) Simplify \(\displaystyle{\frac{n^{-7}}{n^{15}}}\) and write your answer without using negative exponents.
(d) Simplify \(\displaystyle{\frac{n^{-7}}{n^{-15}}}\) and write your answer without using negative exponents.
Hint.
Recall the exponent property: \(\displaystyle \frac{B^m}{B^n} = B^{(m-n)}\)
Also remember that results with negative exponents may be rewritten as \(B^{(-p)} = \frac{1}{B^p}\)
Answer 1.
\(\frac{1}{n^{8}}\)
Answer 2.
Answer 3.
\(\frac{1}{n^{22}}\)
Answer 4.
Solution.
Part (a):
\(\frac{n^{7} }{ n^{15}} = n^{(7-15)} = n^{-8} = \frac{1}{n^{8}}\)
Part (b):
\(\frac{n^{7} }{ n^{-15}} = n^{(7-(-15))} = n^{22}\)
Part (c):
\(\frac{n^{-7} }{ n^{15}} = n^{(-7-15)} = n^{-22} = \frac{1}{n^{22}}\)
Part (d):
\(\frac{n^{-7} }{ n^{-15}} = n^{(-7-(-15))} = n^{8}\)